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CQ bisects <ACD , OA =(OB x OD)(OC + CD), O intersection of diagonals of ABCD

Source: Indonesia INAMO Shortlist 2009 G7 https://artofproblemsolving.com/community/c1101409_

December 11, 2021
angle bisectorgeometry

Problem Statement

Given a convex quadrilateral ABCDABCD, such that OA=OB⋅ODOC+CDOA = \frac{OB \cdot OD}{OC + CD} where OO is the intersection of the two diagonals. The circumcircle of triangle ABCABC intersects BDBD at point QQ. Prove that CQCQ bisects ∠ACD\angle ACD
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